17-11-2018 HSST MATHEMATICS JUNIOR

HSST MATHEMATICS JUNIOR

EXAM DATE:17-11-2018

1.In which year Rabindranath Tagore visited Sivagiri and met Sree Narayana Guru?

A.1925

B.1922

C.1924

D.1920

Ans:B

2.Founder of ‘Atmavidyasangam’was;

A.Ayyankali

B.Pandit Karuppan

C.Vagbhatananda

D.Kumara Gurudevan

Ans:C

3.The social reformer who founded ‘Nizhalthankals’was;

A.Sahodaran Ayyappan

B.Thycaud Ayya Guru

C.Vaikunda Swamikal

D.Chattampi Swamikal

Ans:C

4.Venue of 2024 Olympic games;

A.Australia

B.Paris

C.Tokyo

D.Quatar

Ans:B

5.Volunter captain of Guruvayur Satyagraha Committee was;

A.K.Kelappan

B.T.K.Madhavan

C.K.Madhavan

D.A.K.Gopalan

Ans:D

6.The state from which Alphons Kannanthanam elected as a member of Rajya Sabha;

A.Madhya Pradesh

B.Gujarat

C.Maharashtra

D.Rajastan

Ans:D

7.Who was the President of the ‘Aikya Kerala Conference’held at Thrissur in 1948?

A.T.K.Madhavan

B.K.Kelappan

C.Pattam Thanu Pillai

D.C.Abdul Rahman

Ans:B

8.The winner of 2017’Jananpith Award’;

A.M.T.Vasudevan Nair

B.Ashapurna Devi

C.Urvashi Bhutalia

D.Krishna Sobti

Ans:D

9.The ‘political lab’ of Mahatma Gandhi was;

A.South Africa

B.Kheda

C.Sabarmathi Ashram

D.Champaran

Ans:A

10.The 2017 FIFA Confederation Cup was won by;

A.Brazil

B.Arjenteena

C.Russia

D.Germany

Ans:D

11.Which of the following does not supplement classroom teaching?

A.Handbook

B.Logbook

C.Reference book

D.Source book

Ans:B

12.In a class best on Physics,most of the students failed in the problem session of the test.In such cases,the teacher should construct and administer

A.Achievement test

B.Attitude scale

C.Diagnostic test

D.Inventory

Ans:C

13.Which is the main purpose of research in education?

A.To help in the personal growth of an individual

B.To increase social status of an individual

C.To help in the individual to become an eminent educationalist

D.To increase job prospects of an individual

Ans:C

14.Identify the method which combines the best of individual laboratory work and the lecture demonstration method

A.Scientific method

B.Heuristic method

C.Dalton plan

D.Assignment method

Ans:D

15.Jigsaw is a method of
A.Collaborative learning

B.Co-operative learning
C.Graphic organiser strategy

D.Problem based learning

Ans:B

16.The data of research is

A.Qualitative only

B.Quantitative only

C.Both(A) and (B)

D.Neither(A) nor(B)

Ans:C

17.Which of the following research types aims at immediate application?

A.Conceptual

B.Empirical

C.Action

D.Fundamental

Ans:C

18.Which of the following educational objective is measured when a teacher asks students to write the summary of a given story?

A.Knowledge

B.Synthesis

C.Application

D.Comprehension

Ans:D

19.Adopting innovative strategies in classroom ensures

A.Active learning

B.Direct learning
C.Group learning
D.Technical learning

Ans:A

20.Giving hints or clues lead the students to correct response is

A.Probing

B.Prompting

C.Redirecting

D.Refocusing

Ans:B

21.How many members retire from Rajya Sabha on the expiration of every second year?

A.1/6

B.1/2

C.1/3

D.2/3

Ans:C

22.------------is a subject included in the Concurrent List.

A.Criminal Law and Procedure

B.Public Health and Sanitation

C.Currency and Coinage

D.Inter-State trade and commerce

Ans:A

23.Article 19(1)(e) of the Indian Constitution is related to

A.Right to assemble peaceably and without arms

B.Right to freedom of speech and expression

C.Right to reside and settle in any part of the territory of India

D.Right to form associations or unions

Ans:C

24.A ‘proclamation of emergency’ issued under Article 352 must be approved by resolutions of both houses of Parliament within

A.Six months

B.One month

C.Three months

D.Two months

Ans:B

25.Which of the following Constitution Amendment Act raised the age of reirement of the members of State Public Service Commission from 60 to 62?

A.The Constitution ‘42^(nd)’Amendment Act

B.The Constitution ‘41^(st)’Amendment Act

C.The Constitution ‘40^(th)’Amendment Act

D.The Constitution ‘44^(th)’Amendment Act

Ans:B

26.Section 10 of the Right to Information Act,2005 is related with

A.Third Party information

B.Constitution of Central Information Commission

C.Exemption from the disclosure of information

D.Severability

Ans:D

27.Whoever contravenes the provisions of Mahatma Gandhi National Rural Employment Guarantee Act shall on conviction be liable to

A.A fine which may extend to three thousand rupees

B.A fine which may extend to five hundred rupees

C.A fine which may extend to one thousand rupees

D.A fine which may extend to two thousand rupees

Ans:C

28.Chairperson and every member of the National Commission for Protection of Child Rights shall hold office for a term of

A.Five years

B.Six years

C.Four years

D.Three years

Ans:D

29.Central Government launched Saansad Adarsh Gram Yojana(SAGY)on

A.’18^(th)’October 2014

B.’11^(th)’October 2014

C.’7^(th)’October 2014

D.’24^(th)’October 2014

Ans:B

30.Which of the following authority is entrusted with the power to make rules for carrying out the purposes of the Environment(Protection)Act,1986?

A.State Legislative Assembly

B.Rajya Sabha

C.Central Government

D.State Government

Ans:C

31.The volume of the solid generated by revolving the region bounded by  y=’sqrt(x)’ and the lines y=1,x=4 about the line y=1 is

A.’(5pi)/(6)’

B.’(7pi)/(6)’

C.’(3pi)/(6)’

D.None of these

Ans:B

32.The area of the ellipse ‘(x^(2))/(a^(2))+(y^(2))/(b^(2))=1’ is

A.’pi’ab

B.’pi’’((a+b)/4)^(2)’’’

C.’pi’’((a+b)/(2))^(2)’

D.’pi(a+b)’

Ans:A

33.The number of tangents than can be drawn from(0,0) to the circle ‘x^(2)+y^(2)-2x-4y-4=0’ is

A.0

B.1

C.2

D.None of these

Ans:A

34.The total number of terminating zeros in 100! Is

A.20

B.21

C.24

D.None of these

Ans:C

35.If ‘1^(st)’ January 2018 is Monday,what will be 2036 January ‘1^(st)’?

A.Monday

B.Tuesday

C.Wednesday

D.None of these

Ans:B

36.For a Boolean Algebra <X,+,.,’>where x={0,1,x,y}; the value of x+y is

A.0

B.x

C.y

D.1

Ans:D

37.Let X be a Boolean Algebra.Then the number of elements in X cannot be

A.2

B.4

C.6

D.8

Ans:C

38.Which of the following graph is not Eulerian?

A.’K_(7)’

B.’K_(9,9)’

C.’K_(9)’

D.None of these

Ans:B

39.Which of the following is a planar graph?

A.’K_(5)’

B.’K_(3,3)’

C.Peterson graph

D.None of these

Ans:D

40.Which of the following graph is not bipartite?

A.A tree with 10 edges

B.’K_(6)’

C.’K_(3,3)’

D.None of these

Ans:B

41.If F is a field,then the number of elements in F cannot be

A.3

B.5

C.15

D.125

Ans:C

42.Which of the following is false about a field F of 81 elements?

A.F has a subfield of 27 elements

B.F has a subfield of 9 elements

C.F has a subfield of 3 elements

D.F has exactly 3 subfields including F

Ans:A

43.Let <F,+,.> be a field of 16 elements.Then <F,+> is isomorphic to

A.’ZZ_(16)’

B.’ZZ_(2)’x’ZZ_(2)’x’ZZ_(4)’

C.’ZZ_(2)’x’ZZ_(8)’

D.’ZZ_(2)’x’ZZ_(2)’x’ZZ_(2)’x’ZZ_(2)’

Ans:D

44.Let G be a non-abelian group.Then order of G can be

A.25

B.35

C.55

D.255

Ans:C

45.Let G=’SL_(4)’(‘ZZ_(3)’)’’,the group of all 4x4 matrices over’ZZ_(3)’ with determinant 1.Then the order of any of its Sylow 3-subgroup is

A.’3^(5)’

B.’3^(6)’

C.’3^(7)’

D.None of these

Ans:B

46.Which of the following is not constructible?

A.20-gon

B.30-gon

C.50-gon

D.60-gon

Ans:C

47.Which of the following is false?

A.There exists a vector space of 81 elements

B.There exists a vector space of 81 elements over a field of  3 elements

C.There exists a vector space of 81 elements over a field of 9 elements

D.There exists a vector space of 81 elements over a field of 27 elements

Ans:D

48.Which of the following linear transformation is invertible?

A.T(x,y)=(2x+y,x+’(1)/(2)’y)

B.T(x,y)=(2x+y,’(1)/(2)’x+y)

C.T(x,y)=(x+’(1)/(2)’y,2x+y)

D.T(x,y)=(x+y,x+y)

Ans:B

49.If the characteristic polynomial of the linear transformation T:’RR^(9)’’->RR^(9)’is ‘x^(9)’+4x+1,then det (T-1)is

A.-6

B.-9

C.-1

D.1

Ans:A

50.If A= Matrix of (0 0 0 0 1)first row,(0 0 0 1 0)second row,(1 0 0 0 0)third row,(0 1 0 0 0)fourth row,(0 0 1 0 0) fifth row,then which is true?

A.’A^(3)’=1

B.’A^(4)’=1

C.’A^(5)’=1

D.’A^(6)’=1

Ans:D

51.Which is the following normed linear space is strictly convex?

A.’RR^(2)’with (parallel line parallel line1)

B.’RR^(2)’with (parallel line parallel line2)

C.’RR^(2)’with parallel line parallel line infinity

D.None of these

Ans:B

52.Which of the following is false?

A.A-B is self adjoint if A and B are so

B.Every unitary operator is normal

C.Every normal operator is self adjoint

D.A+B is self adjoint if A and B are so

Ans.C

53.Which of the following is a Hilbert space?

A.’I^(1)’

B.’I^(2)’

C.’I^(00)’

D.None of these

Ans:B

54.Let f(x,y)=’{((x^(3))/(x^(3)+y^(2)) if (x,y)!=(0,0)),(0 if (x,y)=(0,0)):}’ Then which is not true?

A.f is continuous at (0,0)

B.Partial derivatives exists at(0,0)

C.Directional derivatives exists at(0,0)

D.Partial derivatives are not bounded functions on ‘RR^(2)’

Ans:D

55.If the vectors I+2j+3k,4i+5j+6k and 5i+mj+9k are coplanar,then the value of m is

A.7

B.6

C.5

D.None of these

Ans:A

56.Let ‘lim_(x->0)f(x)/x=1’,where 0<’1’’<00’.Then ‘lim_(x->0)’’f(x)’

A.Is always 0

B.Need not exists

C.Exists,but not always zero

D.Exists and depends on’I’

Ans:A

57.Which of the following function is not differentiable on’(0,(pi)/(2))’?>

A.Sin x

B.|sin x|

C.max{ sin x,cos x}

D.None of these

Ans:C

58.Let A be a 5x4 matrix and B be a 4x5 matrix.Then 1 is necessarily an eigen value of

A.AB

B.AB+1

C.BA

D.BA+1

Ans:B

59.The equation ‘x^(2)’+’y^(2)’+2xy-1=0 represents

A.Parabola

B.Ellipse

C.Hyperbola

D.Pair of straight lines

Ans:D

60.Which of the following is not a Banach space?

A.’C_(00)’

B.’I^(oo)’

C.’I^(2)’

D.None of these

Ans:A

61.Which is false about ‘NN’?

A.’NN’cannot be written as a denumerable union of denumerable disjoint sets
B.’NN’ is well ordered

C.’NN’ is a closed subset of ‘RR’

D.None of these

Ans:A

62.E={p’in’’QQ’:2<’p^(2)’<3}.Then which is false?

A.E is open in ‘QQ’

B.E is closed in ‘QQ’
C.E is a bounded subset of ‘QQ’

D.E is a compact subset of ‘QQ’

Ans:D

63.Let function n(x)={(n-1)x raise to n, if x is rational(first row),1-(n-1)x raise to n,if x is irrational(second row).Then which of the following function is discontinuous everywhere on [0,1]?

A.’g_(1)’

B.’g_(2)’

C.’g_(3)’

D.All of these

Ans:A

64.Let f(x)={ x+x raise to 2 sin 1/x,if x not equal to 0(first row),0 if x=0(second row)

The f’(0) is

A.0

B.1

C.2

D.Does not exists

Ans:B

65.Which of the following is not uniformly continuous on ‘RR’?

A.x

B.sin x

C.x sin x

D.’(1)/(1+x^(2))’

Ans:C

66.Let ‘s_(n)’=’1/1^(2)+1/2^(2)+….+1/(n^(2))’.Then which is false?

A.{‘s_(n)’} is a sequence in ‘QQ’

B.{‘s_(n)’} is a Cauchy sequency in ‘QQ’

C.{‘s_(n)’} is convergent in ‘QQ’

D.None of these

Ans:C

67.Let ‘f_(n)’:’RR’’->’’RR’ defined by fn(x)={0 if x elements of (- infinity,n)(first row),n,if x elements of [n,infinity)

Then choose the most correct answer

A.’{f_(n)}’ does not convergent on ‘RR’

B.’{f_(n)}’ converges to zero function on ‘RR’

C.’{‘f_(n)’}converges to zero function on ‘RR’ uniformly

D.None of these

Ans:B

68.Which is false?

A.There exists a function f:’RR’’->’’RR’ which is continuous exactly at one point

B.There exists a function f:’RR’’->RR’ which is differentiable exactly at one point

C.There exists a function f:’RR’’->’’RR’ which is discontinuous everywhere

D.None of these

Ans:D

69.Which of the following subset of ‘RR^(3)’has positive Lebesgue measure?

A.{(x,y,z)’in ‘’RR^(3)’:’x^(2)’+’y^(2)’+’z^(2)’=1}

B.{(x,y,z)’inRR^(3)’:x+y+z=1}

C.’W_(1)’+’W_(2)’+’W_(3)’ where’W_(1)’={(x,x,-x):x’in RR’},’W_(2)’={(x,-x,x):x’in’’RR’},’W_(3)’={(-x,x,x):x ‘in’’RR’}

D.None of these

Ans:C

70.If ‘int_(1)^(00)’f(x) dx=L where 0<L<’oo’;then ‘lim_(x->oo)’f(x)is

A.0

B.’oo’’’

C.Always exists

D.Need not exists

Ans:D

71.Which is false?

A.cos z=5 has a solution in ‘CC’

B.sin z is a polynomial in ‘CC’

C.’sin ^(z)’+’cos z^(2)’=1 for all z ‘in’’CC’

D.Every non constant polynomial in ‘CC’[x] has a zero in ‘CC’

Ans:B

72.The image of the line y=1 under the mapping w=sin z is

A.Parabola

B.Ellipse

C.Rectangular Hyperbola

D.None of these

Ans:B

73.The value of ‘’’int_(C)’’(1)/(z^(3)(z+1)’ dz where C is |z|=3;is

A.2’pi’i

B.-4’pi’i

C.4’pi’i

D.0

Ans:D

74.Consider the metric space (‘NN’,d)where d is given by d(m,n)=|’1/m’-‘1/n’|.Then which is false?

A.d is a bounded metric on ‘NN’

B.d induces the discrete topology on ‘NN’

C.’{1/n}’ converges to 0

D.This space is Hausdorff

Ans:C

75.Which is not a productive property?

A.Connectedness

B.Compactness

C.Locally connectedness

D.Path connectedness

Ans:C

76.Let X=(0,1) and Y=’RR’.Then which is true?

A.X and Y are the same as metric spaces

B.X and Y are the same as topological spaces

C.Both (a) and (b)

D.Neither (a) nor(b)

Ans:B

77.Which of the following topological property is not preserved under a continuous function?

A.Connectedness

B.Compactness

C.First countability

D.None of these

Ans:C

78.Which is true?

A.On’RR’co-finite topology is weaker than usual topology

B.On’RR’usual topology is weaker than co-finite topology

C.On’RR’ co-finite topology and usual topology are not comparable

D.On’RR’co-finite topology and usual topology are the same

Ans:A

79.If every closed interval[a,b] with a<b is open with respect to some topology on’RR’;then with respect to this topology,closure of [27,37]is

A.[27,37]

B.(-‘oo’,37]

C.[27,’oo’)

D.’RR’

Ans:A

80.For the space ‘RR’with co-countable topology,which is false?

A.Uniqueness of limits exists in this space for the convergence of sequences

B.This space is not Hausdorff

C.{‘1/n’} is divergent in this space’’

D.None of these

Ans:D

81.If f:’RR’’->’’RR’ is a twice differentiable function with ‘lim_(x->oo)’(2f(x)+3f’(x))=0 with ‘lim_(x->oo)’f(x)=’lim_(x->oo)’f’(x)=1;then ‘lim_(x->oo)’f’’(x)is

A.0

B.1

C.10

D.11

Ans:D

82.The third approximation ‘y_(3)’(x) for the I.V.P.,y’=2x(1+y);y(0)=0 by Pickard’s method is

A.’x’+’x^(2)/2’+’x^(3)/6’

B.’x^(2)’+’x^(4)/2’+’x^(6)/6’

C.’x’+’x^(2)/2+x^(8)/6’

D.None of these

Ans:B

83.Consider the vector space V={f:’RR’’->’’RR’ such that f’’-2f’+f=0 over ‘RR’.Then which of the following is a basis for V?

A.{‘e^(t)’}

B.{‘e^(t),te^(t)’}

C.{e^(-t)’}

D.None of these

Ans:B

84.If F(a,b,c,x) is the hyper geometric series,then ‘lim_(b->oo)’F(a,b,a,’x/b’)is

A.’(1+x)^(a)’

B.log(1+x)

C.’e^(x)’

D.sin x

Ans:C

85.If ‘P_(n)(x)’ is the Legendre Polynomial ,then ‘P_(n)(-1)’is

A.1

B.-1

C.’(-1)^(n)’

D.0

Ans:C

86.The equation ‘U_(xxxx_)+x^(2)U_(yy)’=0 is

A.Elliptic

B.Parabolic

C.Hyperbolic

D.None of these

Ans:A

87.If a,b,c are three constants such that ‘U_(x)’=a,’U_(y)’=b and ‘U_(z)’=c with u(x,y,z)=0 at (0,0,0); then U(1,0,0)is

A.a

B.b

C.c

D.None of these

Ans:A

88.If 0<s<1,then ‘int_0^oo(x^(s-1))/(1+x)dx’is

A.’beta’(1,s)

B.’beta’(1-s,1)

C.’beta’(1-s,s)

D.Divergent

Ans:C

89.The Laplace transform L{‘(sin omegat)/(t)’} is

A.’cot^(-1)((s)/(w))’

B.’(omega)/(s^(2)+omega^(2))’

C.’(s)/(s^(2)+omega^(2))’

D.None of these

Ans:A

90.Which of the following is a periodic function on ‘RR’?

A.x-[x]

B.x

C.[x]

D.none of these

Ans:A

91.A velocity field is given by q( raist to bar)=xi+(y+t)j.Then the stream line for this field at t=2 is

A.Circle

B.Ellipse

C.Hyperbola

D.Rectangular hyperbola

Ans:D

92.Consider the fuzzy sets A and B on X=[0,’(pi)/(2)’]where A(x)=sin x and B(x)=cos x.Then o.8-cut of A’nn’B is

A.’Phi’

B.X

C.An uncountable subset of X

D.A denumerable subset of X

Ans:A

93.Which is false about the Cantor set?
A.Cantor set is perfect

B.Cantor set is compact

C.Cantor set is fractal

D.Cantor set is an uncountable set with positive Lebesgue measure

Ans:D

94.The Voltra integral equation corresponding to the differential equation y”+xy=1,y(0)=y’(0)=0 is

A.’y(x)’=’(x^(2))/(2)’-‘int_0^xty(t)dt’

B.’y(x)=x^(2)/2’-‘int_0^x(x-t)y(t)dt’

C.’y(x)=(x^(2))/(2)-‘int _0^(x)(x-t)ty(t)dt’

D.’y(x)=(x)/(2)’-‘int_0^x(x-t)ty(t)dt’

Ans:C

95.The derivative of the Weierstrass function is

A.Elliptic

B.Even

C.Pole of order 2

D.All the above

Ans:A

96.The function ‘zeta’ (z)is

A.Weierstrass (z)

B.Weierstrass raise to 1(z)

C.-Weierstrass raise to 1(z)

D.Weierstrass (z)

Ans:D

97.For the Euler’s gamma function symbol(z)symbol(1-z)is

A.’(pi)/(cospiz)’

B.’(pi)/(sinpiz)’

C.’(pi)/(cotpiz)’

D.None of these

Ans:B

98.Which of the following is not a maximal geodesic for the cylinder ‘x_(1)^(2)’+’x_(2)^(2)’=1 in ‘RR^(3)’?

A.Vertical line

B.Horizontal circle

C.Helix

D.None of these

Ans:D

99.Which of the following linear transformation is a possible Weingarten map for the unit n-sphere ‘x_(1)^(2)+’’x_(2)^(2)’+’x_(3)^(2)’=1 in ‘RR^(3)’ oriented by its inward unit normal?

A.T  raise to x bar=0

B.T raise to x bar=x bar

C.T raise to x bar=2 x bar

D.T raise to x bar=3 x bar

Ans:B

100.Which of the following is reducible over ‘RR’?

A.’x^(2)’+1

B.’x^(2)’+2

C.’x^(5)’+’x^(3)+’’x^(2)’+x+1

D.None of these

Ans:C

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